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Random matrix analysis of network Laplacians

Author

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  • Jalan, Sarika
  • Bandyopadhyay, Jayendra N.

Abstract

We analyse the eigenvalue fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that the nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of the random matrix theory. Furthermore, we study the nearest neighbor spacing distribution as a function of the random connections and find that the transition to the Gaussian orthogonal ensemble statistics occurs at the small-world transition.

Suggested Citation

  • Jalan, Sarika & Bandyopadhyay, Jayendra N., 2008. "Random matrix analysis of network Laplacians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 667-674.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:2:p:667-674
    DOI: 10.1016/j.physa.2007.09.026
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    Cited by:

    1. Zhan, Choujun & Chen, Guanrong & Yeung, Lam F., 2010. "On the distributions of Laplacian eigenvalues versus node degrees in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1779-1788.
    2. Maiorino, Enrico & Rizzi, Antonello & Sadeghian, Alireza & Giuliani, Alessandro, 2017. "Spectral reconstruction of protein contact networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 804-817.

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